Biotransport: Fluid Mechanics, Heat and Mass Transfer Dr. Portonovo S. Ayyaswamy Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania

Abstract There is an important need for comprehensive courses related to Biotransport to be offered at the undergraduate and graduate levels in US Universities. These courses must emphasize both theory and applications, motivating students to carry out careful experimentation which will validate what they have learned in theory. At present, although there are many different descriptions of courses related to biotransport that are available in catalogues of various departments, it is clear that a systematic approach is needed to develop a formally comprehensive set of guidelines and course material descriptions that will be useful for the student body at large.

Abstract (cont’d) As a part of this discussion, a comprehensive model course description is displayed in the following. This model will apply to undergraduate and graduate level courses; the degree of detail, rigor, and emphasis will vary depending on the level at which the course is offered.

Introduction to Biotransport The role of transport processes in biological systems; biological system description must include precise concepts both from biology and from engineering. What constitutes a biological system model must be addressed. Multiphase (both on the basis of material composition and thermodynamically distinct phases) are common in biotransport. Diffusion, convection, binding interactions, and cellular transport are the most common types and must be clearly discussed. Plane view of a bubble in blood flow, Trigger, cause, activate, surfactant treatment, motivation

Introduction to Biotransport (cont’d) Transport within cells and across membranes Physiological transport systems: Consideration may be limited to the cardiovascular system and the respiratory system since they are well understood.

Review of Fundamentals of Fluid Mechanics Review of fluid properties and their ranges as functions of pressure and temperature Newtonian and non-Newtonian fluids: limits where fluids may be considered Newtonian to an excellent approximation Fluid statics, fluid kinematics; relevance to transport phenomena Laminar and turbulent flows as illustrated by examples taken from systems

Review of Fundamentals of Fluid Mechanics (cont’d) Lagrangian and Eulerian view points of fluid flow; why are these important and where such descriptions are suitable Compressible and incompressible flows; examples of systems where this distinction is critical Inviscid and Irrotational Flows; Bernoulli and Euler equations; examples in systems where these offer suitable descriptions

Review of Conservation Relations in Integral and Differential Forms Control volume; fixed and moving; frames of reference Basic equations in integral form, Reynolds transport equation Applicable boundary (interface) and initial conditions Review of differential forms of the equation of conservation of mass, linear momentum and Navier-Stokes equation Fluid motion with more than one dependent variable Low, intermediate and high Reynolds-number flows Photos provided by Presbyterian Healthcare System, 8200 Walnut Hill Ln., Dallas, TX 75231, Juan Carlos Reynoso, Communications Resource Center. http://www.wound.com/chamout.html

Blood Rheology: Properties of Flowing Blood Blood composition, viscosity, yield stress, Fahraeus-Lindqvist effect Power-law model, Casson model, Carreau-Yasuda model Usefulness and shortcomings of existing models Blood vessel structure

Circulatory Biofluid Mechanics Systemic and Pulmonary circulations Inviscid approximations; viscous flows and boundary layer theory Flow separation; examples from systems Lubrication theory; limits of applicability Peristaltic pumping

Fluid Flow in the Circulation and Tissues Introduction Oscillating flow in a cylindrical tube Entrance lengths Flow in curved vessels Flow in branching vessels

Fluid Flow in the Circulation and Tissues (cont’d) Flow in arteries Flow in collapsible tubes Heart-valve Hemodynamics Introduction to non-Newtonian flows in tubes Use of models in flow descriptions, arterial fluid dynamics

Mass Transport in Biological Systems Introduction Solute fluxes in mixtures Conservation relations, Fick’s laws Steady and unsteady diffusion Diffusion-limited reactions, equimolar counter diffusion Lumped parameter techniques; Compartmental models with pharmokinetics

Mass Transport in Biological systems (cont’d) Transport across membranes Conservation of mass for dilute solutions Dimensional analysis Electrolyte transport, diffusion and convection Mass transfer coefficients Mass transfer across membranes

Transport in Porous Media Introduction Porosity Toruosity, and available volume fraction Fluid flow in porous media Solute transport in porous media Fluid transport in poroelastic materials

Introduction to Molecular Transport Within Cells Receptors and Ligands Binding kinetics, rate constants, endocytosis, signal transduction, gene expression Cell attachment and detachment Rolling and adhesion

Introduction to Bio Heat Transfer Basic concepts Conservation of energy equation; thermal effects; role of Prandtl number Heat transfer to blood vessels Equilibration lengths Models of perfused tissues, continuum models, Pennes heat sink model, directed perfusion model, effective conductivity model, combination models

Introduction to Bio Heat Transfer (cont’d) Parameter values Solutions of continuum models Treatment of boundary conditions Vascular geometry generating algorithms Solution of coupled tissue-vascular models Statistical interpretation

Applications of Theory Elasticity in Biomechanics Extension Compression Simple shear of soft tissue Extension and torsion of a papillary muscle Analysis of stress, strain and deformation

Recommended Books (1) Transport Phenomena in Biological Systems by G.A. Truskey, F. Yuan and D. F. Katz, Pearson Prentice Hall, 2004. (2) Biofluid Mechanics—The Human Circulation by K.B. Chandran, A.P. Yoganathan, and S.E. Rittgers, Taylor & Francis, 2007. (3) Biomechanics: Mechanical Properties of Living Tissues by Y.C. Fung, Second Edition, Springer, 1993. (4) Biomechanics: Circulation by Y.C. Fung, Second Edition, Springer, 1997. (5) Biofluid Dynamics: Principles and Selected Applications by C. Kleinstreuer, Taylor and Francis, 2006. (6) Biofluid Mechanics by J.N. Mazumdar, World Scientific, 2004.

Recommended Books (cont’d) (7) The Fluid Mechanics of Large Blood Vessels by T.J. Pedley, Cambridge Univ. Press, 1980. (8) Introduction to Bioengineering by S.A. Berger, W. Goldsmith and E.R. Lewis, Oxford, 1996. (9) Nonlinear theory of elasticity: Applications in biomechanics by L.A. Taber, World Scientific, 2004. (10) Basic Transport Phenomena in Biomedical Engineering by R.L. Fournier, Taylor and Francis, 2007. (11) Introduction to Biofluid Mechanics by P.S. Ayyaswamy, Chapter 17 in Fluid Mechanics by P.K. Kundu and I.M. Cohen, Elsevier, 2008. (12) Analysis of Transport Phenomena by William M. Deen, Oxford, 1998.